On February 1, 2013, Janet buys a bond for $10,000 that makes coupon payments of $600 after each of the following two years and returns its principal of $10,000 at the end of the second year. In other words, it is a standard coupon bond with a 6 percent annual interest rate making payments once each year.On February 1, 2014, Janet receives her first coupon payment of $600. At that time, the market interest rate on bonds like hers has fallen to 4 percent. She sells her bond to Justin at that time, for a price equal to the present value of the bond's payments.
a.How much does Justin pay Janet for the bond?Both Janet and Justin have tax rates of 30 percent on interest income and 20 percent on capital gains. (Note that if someone has a capital loss, you may assume that he or she can reduce taxes by the amount of the capital loss times the tax rate of 20 percent.)
b.Calculate Janet's after-tax rate of return for the past year (from Feb. 1, 2013, to Feb. 1, 2014).Justin holds onto the bond from February 1, 2014, to February 1, 2015, so it matures and he receives the second coupon payment and the principal.
c.What is Justin's after-tax rate of return for the year from Feb. 1, 2014, to Feb. 1, 2015?Explain and show all your work for each part. You may assume, of course, that the market works and does not malfunction.
What will be an ideal response?
| a. | The bond has one year left to maturity, which pays interest of $600 and repays principal of $10,000, so the price of the bond is | |
 . | ||
| b. | Her total return consists of current yield plus capital-gain yield. Doing these in after-tax terms means subtracting off the taxes for each. | |
| Interest payment = $600 | ||
| Tax on interest payment = $600 × 0.3 = $180 | ||
| Interest after taxes = $600 ? $180 = $420 | ||
After-tax current yield =  = 0.042 = 4.2% | ||
| Capital gains = $10,192.31 ? $10,000 = $192.31 | ||
| Tax on capital gains = $192.31 × 0.2 = $38.46 | ||
| Capital gains after taxes = $192.31 ? $38.46 = $153.85 | ||
After-tax capital-gains yield =  = 0.015 = 1.5% | ||
| Total after-tax return | = after-tax current yield + after-tax capital-gains yield | |
| = 4.2% + 1.5% | ||
| = 5.7% | ||
| c. | Justin gets $600 in interest, so his interest after taxes is the same as Janet's was, which is $420. But he paid more, so his current yield will be lower: | |
After-tax current yield =  = 0.041 = 4.1% | ||
| Justin gets a capital loss because he bought the bond for $10,192.31 and it pays only $10,000 when it matures. | ||
| Capital gains = $10,000 ? $10,192.31 = ?$192.31 | ||
| Tax on capital gains = ?$192.31 × 0.2 = ?$38.46 | ||
| Capital gains after taxes = ?$192.31 ? (?$38.46) = ?$153.85 | ||
After-tax capital-gains yield =  = ?0.015 = ?1.5% | ||
| Total after-tax return | = after-tax current yield + after-tax capital-gains yield | |
| = 4.2% + (?1.5%) | ||
| = 2.6% | ||
You might also like to view...
In the job characteristics model, ______ is the extent to which employees are given freedom and independence to schedule and perform tasks.
What will be an ideal response?
The overall objective of the scope management plan is to document and inform project stakeholders about the project, what tools will be used, and how they will be applied by the project to ensure success
Indicate whether the statement is true or false
An idealistic vision can arouse employee enthusiasm and therefore is a good vision.
Answer the following statement true (T) or false (F)
Ollie, an employee of Payroll Management Corporation, is arrested at work. A grand jury issues a formal charge against Ollie for larceny. This charge is
A. an arraignment. B. an indictment. C. an information. D. an inquisition.